Schramm-Loewner evolution and perimeter of percolation clusters of correlated random landscapes

Motivated by the fact that many physical landscapes are characterized by long-range height-height correlations that are quantified by the Hurst exponent H, we investigate the statistical properties of the iso-height lines of correlated surfaces in the framework of Schramm-Loewner evolution (SLE). We...

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Bibliographic Details
Published in:arXiv.org 2017-12
Main Authors: de Castro, Caio P, Lukovic, Mirko, Pompanin, Giacomo, Andrade, Roberto F S, Herrmann, Hans J
Format: Article
Language:English
Subjects:
Correlation
Evolution
Landscape
Markov processes
Percolation
Online Access:Get full text
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Summary:Motivated by the fact that many physical landscapes are characterized by long-range height-height correlations that are quantified by the Hurst exponent H, we investigate the statistical properties of the iso-height lines of correlated surfaces in the framework of Schramm-Loewner evolution (SLE). We show numerically that in the continuum limit the external perimeter of a percolating cluster of correlated surfaces with H between -1 and zero is statistically equivalent to SLE curves. Our results suggest that the external perimeter also retains the Markovian properties, confirmed by the absence of time correlations in the driving function and the fact that the latter is Gaussian distributed for any specific time. We also confirm that for all H the variance of the winding angle grows logarithmically with size.
ISSN:2331-8422
DOI:10.48550/arxiv.1712.03115